Methodological framework to develop the shoreline erosion model
This study applies both the Bruun model and statistical methods to investigate coastal hazards. The Bruun model connects the sea level rise with erosion retreat processes in three dimensions. Erosion and recession are frequently used interchangeably in this research. Thus, recession refers to the landward displacement of shoreline whereas erosion denotes the disintegration of land and volumetric change in the coast, albeit recession could be a consequence of shoreline erosion. The Bruun model was applied on data from 20 transects in the Kuala Terengganu sandy beach area to predict the evolution of sandy beach relative to sea-level rise. The sandy beach erosion model depends on predicted rates of sea level change, coastal measurement data and historical data of shoreline change. The use of statistics and computer-based approaches alongside the predicted and observed data enhance the forecasting of erosion with a simple mathematical model (Bruun model). This section discusses the diverse methods and techniques which are applied in this study to evaluate coastal erosion.
Figure 1 illustrates the four components of our methodology. Firstly, beach data were collected along transects in Kuala Terengganu's sandy beach region. Samples from each transect were analyzed for particle size as the Bruun model can only be used for sand (Gale and Hoare, 2012). Also a beach profile was produced for each transect. Secondly, we developed the structure of the Bruun model and forecast erosion for the sandy beaches. Thirdly, sand transportation was estimated for each transect. Finally, we validated the results of the Bruun model using historical and statistical data.
Study area
Terengganu is a state of Peninsular Malaysia. The coastal city of Kuala Terengganu is located by the Terengganu River estuary about 500 km Northeast of Kuala Lumpur on a promontory surrounded on three sides by the South China Sea. It is the state and royal capital as well as the largest city in Terengganu, providing home to a population of 286,317 residents. Kuala Terengganu is the tourism gateway to the East Coast Economic Region (ECER) and thus holds great economic importance for the area. Figure 2 shows our transects and erosion locations.
The Kuala Terengganu coastline in Malaysia is impacted on by natural forces largely governed by the Southwest monsoon (May to September) and the Northeast monsoon (October to March). The Northeast monsoon triggers Malaysia's major rainy season and powerful waves, with monsoon winds impacting the volume and direction of the waves (Maged and Ibrahim, 1996). Natural forces including waves, wind, and currents move unconsolidated soils and sand up the coast which leads to rapid variation in shoreline positions (Morton, 2005). The tidal range along Peninsular Malaysia's east coast, as well as the yearly variations in the average sea level, are estimated to be in the order of 1–2 meters, with wave not exceeding a height of more than 1.8m (Husain et al., 1995a). The variations in beach profile that occur between non-monsoon and monsoon seasons have proven useful in explaining the sequential changes that occur on beaches during monsoon seasons (Rosnan et al., 1995). The east coast of Peninsular Malaysia is more vulnerable to coastal changes, owing to the greater influence of the Northeast monsoon compared to the Southwest monsoon. Kuala Terengganu is one of the locations along Malaysia's east coast that is threatened by significant coastline erosion (Ariffin and Helmy, 2017) as the whole Peninsular is susceptible to sea-level rise (Chalabi et al., 2006; Ibrahim and Wibowo., 2013). Several studies have been conducted by National Hydraulic Research Institute of Malaysia (NAHRIM) around this issue yielding coastal vulnerability assessments and inundation maps (Awang and Abd. Hamid, 2013). Ishak et al. (2014) noted that over 70% of Terengganu was classified as a low-lying coastal area of less than 200 m in altitude, and about 30% of the area was considered vulnerable to flash floods. The Northeast monsoon has also triggered flooding in Southern Thailand and other parts of Malaysia (Gasim et al., 2007), exacerbating the potential vulnerability, hazard, and risk to coastal cities in these countries. Thus there is great need for research on coastal assessments and analysis, shoreline alterations, historical mapping, and shoreline position forecasting to support the planning of coastal development setbacks.
Data collection
Data from various sources were obtained as per Table 1. Field data were collected during the Northeast (NE) monsoon from 6th October to 26th October 2015. The 20 transects were chosen because they are prone to severe erosion (DMRS and PAGASA, 2014).
Table 1
Bruun model data collection and sources.
Type of data
|
Beach and Marine Data
|
Resolution
|
Source
|
Primary data
|
20 transects and GPS-surveyed data
|
Beach Measurement data For 20 transects
|
-
|
Fieldwork survey
Kuala Terengganu
|
Land-based photo data for each transect
|
-
|
-
|
Fieldwork survey
Kuala Terengganu
|
Sand particle size data for each transect
|
-
|
-
|
Fieldwork survey
Kuala Terengganu
|
Secondary data
|
Spatial data
|
Topography 2005 and Hydrographic 2005 Maps
|
1:50000
|
JUPEM and Navy
|
Air photos of 1980 and 2005
|
1:5000 1:10000
|
JUPEM
|
Non-spatial data
|
Oceanographic data
|
-
|
Report from some agency of Malaysia
|
Technical report
|
-
|
Report from some agency of Malaysia
|
All data were collected during low tides for each of the 20 transects. Clinometers were used to measure the angle, sand samples taken for particle size measurements, transect distances measured, a Garmin eTrex used to collect coordinates of each transect (GPS accuracy: 15 m, 95% typical, and velocity: 0.05 m/s steady state, DGPS (WAAS) accuracy) and photographs taken of all transects (Fig. 3). The sand samples (weighing between 2.5 and 2.8 kg each) were taken from the center of each transect line using a stake, slender, and hammer and analysed in the laboratory for particle size measurement.
To determine particle size a sand sieve analysis was carried out using a conventional dry sieving process. The material was washed and dried in a laboratory oven set to 105 to 110°C. Following that, 20 dry sand samples of a known weight were passed through a set of 5 suitable sieves with a known mesh size. For ten minutes, the sieves were mechanically shook. Finally, the researchers calculated the weight of sand retained on each sieve as a percentage of the total weight of the sand sample (Bruun, 1962).
Using the following method in Excel (Eqs. 1 and 2), we computed the slope and elevation for each transect using measured distance and angle obtained during fieldwork:
Slope = Distance * Cosine [Radian (Angle)] (1)
Elevation=Distance * Sine [Radian (Angle)] (2)
By using slope, elevation, and distance, we drew the beach profile for each transect in Excel.
The Bruun model
The Bruun model signifies a simple profile transition technique that was proposed for the estimation of the net sand loss on the profile of beaches (Fenster, 2005). Dubois (1992) first proposed that contemporary beach erosion rates are caused by rising sea levels, and as a result, the Bruun model (Bruun, P., 1954) illustrates the relationship between rising sea levels and coastal retreat, and captures the percentage of horizontal to vertical active profile measures (Dolan, 1991). The Bruun model links the two-dimensional shoreline reaction (vertical and horizontal) to sea-level rise. It has offered the scientific and engineering communities a valuable technique of interpreting shoreline changes and proved a valuable tool for planning beach stabilization projects (Schwartz, 1967). The Bruun model had been validated in field tests and literature as examined by Bruun (1988). The model is also referred to as the Bruun's rule (Zhang, 1998).
According to the model, as sea level rises the cross-shore form of the beach profile takes on an equilibrium shape that turns landward and upward (Eq. 3). According to the bathymetry map and offshore wave, the first segment of this model is used to compute the extent of the depth of the closer (h*) active zone (L) near the coastline. The second section inspects the extent of the shoreline retreat under various sea-level rise scenarios. The coastline shift predicted in this research is based on the outcome of the rise in sea level, which is explained in Chap. 3.
The following is a mathematical representation of the model:
\(\text{R}=\text{G}.\frac{\text{L}}{\text{B}+{\text{h}}^{\text{*}}}.\text{S}\) (3)
where \(R\) represents the shore’s horizontal retreat; \({\text{h}}^{\text{*}}\) signifies the depth of closure or depth where the residue interchanges between the shoreface and inner shelf which is presumed to be marginal; \(B\) represents the berm’s height;\(L\) signifies the beach profile’s length to \({\text{h}}^{\text{*}}\); \(S\) represents the vertical sea level rise and \(G\) signifies the inverse of the eroded material’s overfill ratio (Fig. 4) (Coelho and Veloso-Gomes, 2006). If the whole research area is a sandy beach, the eroded material (G) is equal to one, according to the Bruun model and prior studies on coastal erosion. As a result of the particle size examination, it was discovered that all 20 transects are indeed sandy. It is necessary to identify the active sediment transport area on the native beach to appropriately determine the requisite volumes for beach nourishment. Anders and Hansen (1990) noted that the distance to closure enhances the determination of the seaward degree of sediment movement.
The depth of closure (DoC) is a practical metric for determining the seaward limit of significant cross-shore sediment movement on sandy beaches. Coastal engineering makes considerable use of it. As a result, the precise position of closure is determined by the depth change criterion used to characterize closure from a set of dimensions. Closure is generally described in terms of measurement accuracy, however there are only a few models that can forecast closure. Nicholas et al., (1998) developed a widely used and well-validated formulation of severe wave conditions in a generalized time-dependent model to calculate the yearly depth of closure (h*) on sandy beaches (Eq. 4). It is given as follows, as updated by (List et al., 1997):
\({\text{h}}^{\text{*}}=2.28{\text{*}\text{H}}_{\text{e}\text{t}}-68.5\text{*}\left(\frac{{\text{H}}_{\text{e}\text{t}}^{2}}{\text{g}\text{*}{\text{T}}_{\text{e}\text{t}}^{2}}\right)\), (4)
where \({\text{h}}^{\text{*}}\) represents the closure’s predicted depth obtained from the observation’s time length t regarding the Mean Low Water (MLW); \({H}_{e}\) signifies the non-breaking greatest local important wave height which ensues for over 12 hours per t years; \({T}_{e}\) represents the connected wave period with \({(H}_{e})\); and \(\text{g}\) signifies the acceleration that occurs because of gravity. This technique specifically knows that the movement of some sediment will happen seaward of \({\text{h}}^{\text{*}}\)(Fig. 4). The Northeast monsoon has a propensity to erode a larger portion of the beach profile due to rising offshore bottom currents and sediment transport, whereas the Southwest monsoon has a tendency to replenish the top profile. Literature shows that there are four seasons in Malaysia including the main season (Northeast monsoon season), low season (Southeast monsoon season), and two interval seasons. The main season is fundamental for the assessment of erosion and flood hazard in coastal regions in Malaysia. Based on the recent (DMRS and PAGASA, 2014), the Peninsular Malaysia East coast suffers from severe erosion during the main season (Northeast monsoon season). Following DoC and some information supplied by the bathymetric map (2005) in Kuala Terengganu, we estimated the active zone of 20 transects. As several transects had berm, the berm height was measured using a beach profile measurement approach. Because the erosion rate for the sandy beach zone is governed by the rate of sea level rise, sea level rise is a critical element in the Bruun model calculation.
The Accuracy of Shoreline Prediction
The Bruun model conclusion may be verified and validated by comparing observed coastal erosion rates to model generated rates (Crowell et al., 1991). The historical coastline data used in this study was derived from JUPEM's historical data of high-resolution air photographs. GIS software was used to do a specific analysis of the historical coastline, which involved geo-referencing using historical images based on a topographical map with a Planimetric Accuracy (x, y) of 25.00 m, and an Altitude Accuracy (z) of 10 m (Arshad 2014). For 1980 and 2005, the calculated RMSE in geo-referencing is around 0.098 and 0.078, respectively. The rates of coastal erosion were calculated using historical data and the Bruun model's simulated data. It is necessary to choose a uniform coordinate grid system to compare mapped shorelines and other mapped or air photo-derived shorelines for all maps and air photos to be appropriately aligned to ensure the most precise determination of previous shoreline movement.
It is necessary to identify numerous solid and permanent locations or features on the map for which exact and current geographic coordinates are established in order to align maps to a certain coordinate system (Khamis and Abdullah, 2014). The prediction error, as well as the explanation of the validation between the predicted and observed data, are frequently used to explain performance evaluation (US Army, 1989). For assessing the performance of erosion in the sandy beach zone, a variety of accuracy assessment methods are used. Here the model's performance was evaluated using the Mean Square Error (MSE) and Correlation determination (R2), which represent the most generally accepted or recognized statistical methods.
Sand Transport Rate on the Long Beach
The rate of transport of littoral material alongshore in the surf zone caused by currents generated by obliquely breaking waves is referred to as the Long Shore Sand Transport (LST) rate. To calculate the whole LST rate, the entire LST rate is considered to be comparable to extended shore energy flow in the surf zone, which is indicated by the Eq. (5) (Bhuiyan and Siwar 2011):
\(\text{Q}=\frac{\text{K}}{\left({{\rho }}_{\text{s}}-{\rho }\right)\text{*}\text{g}\text{*}{\text{a}}^{{\prime }}}\text{*}{\text{P}}_{\text{l}\text{s}}\) (5)
where (K) represents a dimensionless empirical sand transport coefficient (K = 0.39 if substantial breaking wave height is utilized to compute Pls); (ρs) represents sand density (ρs = 2.650 kg/m3); (ρ) signifies water density (seawater at 20° C, ρ = 1,025 kg/m3); (g) denotes the acceleration caused by gravity (g = 9.81 m/s2); (a′) represents the proportion of the volume of solids to overall volume (accounting for the porosity of the sand (a′ = 0.6)), and (Pls) denotes the longshore wave energy flux factor.